Murray reached the Wimbledon and US Open finals with John Peers in 2015.
"I'm starting to get the hang of this game, I think," said Murray.
"It took me a long time to understand what it took to win, and to perform at optimum level every time you step on the court.
"I've been lucky, I had a great partner for the last few years in John Peers and am now starting a new journey with Bruno here.
"It's been a great two weeks for us and hopefully with one more match we can get over the final hurdle.